Random Schr\"odinger operators with a background potential

TL;DR

This paper investigates one-dimensional random Schr"odinger operators with background potentials, analyzing their spectral properties, proving Anderson Localization for broader classes, and deriving the integrated density of states.

Contribution

It introduces new results on the influence of background potentials on the spectrum and localization, extending previous understanding in one-dimensional random Schr"odinger operators.

Findings

Proved Anderson Localization for a larger class of operators

Established existence of the integrated density of states

Derived a formula for the integrated density of states

Abstract

We consider one-dimensional random Schr\"odinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schr\"odinger operator and obtain Anderson Localization for a larger class of one-dimensional Schr\"odinger operators. Further, we prove the existence of the integrated density of states and give a formula for it.